Partial charge transfer and absence of induced magnetization in $\mathrm{EuS}\left(111\right)/{\mathrm{Bi}}_2{\mathrm{Se}}_3$ heterostructures

Heterostructures made from topological and magnetic insulators promise to form excellent platforms for new electronic and spintronic functionalities mediated by interfacial effects. We report the results of a first-principles density functional theory study of the geometric, electronic structure, and magnetic properties of the $\mathrm{EuS}\left(111\right)/{\mathrm{Bi}}_2{\mathrm{Se}}_3$ interface, including van der Waals and relativistic spin-orbit effects. In contrast to previous theoretical studies, we find no appreciable magnetic anisotropy in such a heterostructure. We also do not see additional induced magnetization at the interface or the magnetic proximity effect on the topological states. This is due to the localized nature of Eu moments and because of a partial charge transfer of $\sim 0.5$ electron from Eu to Se. The formation of the surface dipole shifts the Dirac cone about 0.4 eV below the chemical potential, and the associated electrostatic screening moves the topological state from the first to the second quintuple layer of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$.

Figure 1

Calculated electronic band structure of bulk (a) EuS(111) and (b) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystals using $\mathrm{PBE}+U$ (with $U_f=10$ eV and $J_f=1$ eV) and DFT-D2 functionals [25], respectively. The left inset shows the first Brillouin zone of a hexagonal lattice [26]. The Fermi level is at zero energy. An indirect electronic band gap, $E_{\text{g}}=1.58$ eV, is obtained for EuS(111), while for ${\mathrm{Bi}}_2{\mathrm{Se}}_3, E_{\text{g}}=0.27$ eV. Zoom-in electronic band structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystal, (c) from 1.3 to 1.6 eV and (d) from $-0.5$ to 0.5 eV in the vicinity of the $\mathrm{\Gamma }$ point.

Figure 2

(a) The first Brillouin zone of a rhombohedral lattice [26]. (b) Calculated surface state spectrum from a bulk ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ rhombohedral unit cell, using the DFT-D2 functional and spin-orbit coupling [25]. The energy region of bulk-projected and topological surface-projected states is indicated by light- and dark-red colors, respectively. The Dirac cone is at zero energy.

Figure 3

(a) Side view of the EuS(111)/seven quintuple layers ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ heterostructure with $a_{\text{EuS(111)}}=4.256 \AA$ and out-of-plane magnetization. Eu, S, Bi, and Se atoms are represented in pink, yellow, purple, and green, respectively. The blue shaded part represents the interface zone. (b) Calculated local potential, (c) charge transfer per unit cell area, and (d) local magnetic moment as a function of the $c$ direction. (e) Charge density transfer at the interface. Yellow represents positive electronic densities which accept electrons and cyan represents negative densities which donate electrons. (f) Two-dimensional charge density transfer at the interface, projected onto the $(1/21/20)$ plane.

Figure 4

Calculated electronic band structure of (a) EuS(111)/ seven quintuple layers (QLs) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and (b) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ slab with seven QLs. The Fermi level is at zero energy. The nontopological Rashba interface state below the chemical potential, the topological interface state, and the quasilinear high-energy state are in red, blue, and orange, respectively.

Figure 5

Atom-projected band structure at the interface of (a) EuS(111)/seven quintuple layers ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ onto (b) Eu-$d$, (c) S-$p$, (d) Bi-$p$, and (e) Se-$p$ orbitals. The size of the filled circles is proportional to the weight projected onto the orbitals. The Fermi level is at zero energy. The blue shaded part represents the interface zone.

Figure 6

Electronic band structure and band-decomposed charge density distributions at the $\mathrm{\Gamma }$ point of EuS/${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and seven quintuple layers ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ for (a) nontopological Rashba interface states below the chemical potential (red lines), (b) topological interface states (blue lines), and (c) quasilinear high-energy states (orange lines). The Fermi level is at zero energy.